Hostname: page-component-5f745c7db-6bmsf Total loading time: 0 Render date: 2025-01-06T06:51:18.295Z Has data issue: true hasContentIssue false

An Upgrading Procedure for Adaptive Assessment of Knowledge

Published online by Cambridge University Press:  01 January 2025

Pasquale Anselmi*
Affiliation:
University of Padua
Egidio Robusto
Affiliation:
University of Padua
Luca Stefanutti
Affiliation:
University of Padua
Debora de Chiusole
Affiliation:
University of Padua
*
Correspondence should be made to Pasquale Anselmi, Department FISPPA, University of Padua, Via Venezia 8, 35131 Padua, Italy. Email: pasquale.anselmi@unipd.it

Abstract

In knowledge space theory, existing adaptive assessment procedures can only be applied when suitable estimates of their parameters are available. In this paper, an iterative procedure is proposed, which upgrades its parameters with the increasing number of assessments. The first assessments are run using parameter values that favor accuracy over efficiency. Subsequent assessments are run using new parameter values estimated on the incomplete response patterns from previous assessments. Parameter estimation is carried out through a new probabilistic model for missing-at-random data. Two simulation studies show that, with the increasing number of assessments, the performance of the proposed procedure approaches that of gold standards.

Type
Article
Copyright
Copyright © 2016 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahlgren Reddy, A., Harper, M. (2013). ALEKS-based placement at the University of Illinois. In Falmagne, J.-C., Albert, D., Doble, C., Eppstein, D., Hu, X. (Eds.), Knowledge spaces: Applications in education (pp. 5168), Berlin: SpringerCrossRefGoogle Scholar
Anselmi, P., Robusto, E., Stefanutti, L. (2012). Uncovering the best skill multimap by constraining the error probabilities of the gain-loss model. Psychometrika, 77, 763781CrossRefGoogle Scholar
Anselmi, P., Robusto, E., Stefanutti, L. (2013). A procedure for identifying the best skill multimap in the gain-loss model. Electronic Notes in Discrete Mathematics, 42, 916CrossRefGoogle Scholar
Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74, 619632CrossRefGoogle Scholar
Cosyn, E., Thiéry, N. (2000). A practical procedure to build a knowledge structure. Journal of Mathematical Psychology, 44, 383407CrossRefGoogle ScholarPubMed
Cosyn, E., Uzun, H.B. (2009). Note on two necessary and sufficient axioms for a well-graded knowledge space. Journal of Mathematical Psychology, 53, 4042CrossRefGoogle Scholar
de Chiusole, D., Stefanutti, L., Anselmi, P., Robusto, E. (2015). Modeling missing data in knowledge space theory. Psychological Methods, 20, 506522CrossRefGoogle ScholarPubMed
de la Torre, J., Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69, 333353CrossRefGoogle Scholar
de la Torre, J., Douglas, J. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika, 73, 595624CrossRefGoogle Scholar
Degreef, E., Doignon, J.-P., Ducamp, A., Falmagne, J-C (1986). Languages for the assessment of knowledge. Journal of Mathematical Psychology, 30, 243256CrossRefGoogle Scholar
Doignon, J.-P. (1994). Knowledge spaces and skill assignments. In Fisher, G.H., Laming, D. (Eds.), Contributions to mathematical psychology, psychometrics and methodology (pp. 111121), Berlin: SpringerCrossRefGoogle Scholar
Doignon, J.-P., Falmagne, J-C (1985). Spaces for the assessment of knowledge. International Journal of Man-Machine Studies, 23, 175196CrossRefGoogle Scholar
Doignon, J.-P., Falmagne, J-C (1999). Knowledge spaces, Berlin: SpringerCrossRefGoogle Scholar
Dowling, C., Hockemeyer, C. (2001). Automata for the assessment of knowledge. IEEE Transactions on Knowledge and Data Engineering, 13, 451461CrossRefGoogle Scholar
Dowling, C.E. (1993). Applying the basis of a knowledge space for controlling the questioning of an expert. Journal of Mathematical Psychology, 37, 2148CrossRefGoogle Scholar
Düntsch, I., Gediga, G. (1995). Skills and knowledge structures. British Journal of Mathematical and Statistical Psychology, 48, 927CrossRefGoogle Scholar
Falmagne, J.-C., Cosyn, E., Doignon, J.-P., & Thiéry, N. (2006). The assessment of knowledge, in theory and in practice. In B. Ganter & L. Kwuida (Eds.), Formal Concept Analysis, 4th International Conference, ICFCA 2006, Dresden, Germany, February 13–17, 2006. Lecture Notes in Artificial Intelligence (pp. 61–79). Berlin: Springer.Google Scholar
Falmagne, J.-C., Doignon, J-P (1988). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 123CrossRefGoogle Scholar
Falmagne, J.-C., & Doignon, J.-P. (1988b). A Markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232258.CrossRefGoogle Scholar
Falmagne, J.-C., Doignon, J-P (2011). Learning spaces: Interdisciplinary applied mathematics, Berlin: SpringerCrossRefGoogle Scholar
Falmagne, J.-C., Koppen, M., Villano, M., Doignon, J-P, Johanessen, L. (1990). Introduction to knowledge spaces: How to build, test and search them. Psychological Review, 97, 204224CrossRefGoogle Scholar
Gediga, G., Düntsch, I. (2002). Skill set analysis in knowledge structures. British Journal of Mathematical and Statistical Psychology, 55, 361384CrossRefGoogle ScholarPubMed
Haertel, E.H. (1989). Using restricted latent class models to map the skill structure of achievement items. Journal of Educational Measurement, 26, 301321CrossRefGoogle Scholar
Heller, J., Repitsch, C. (2012). Exploiting prior information in stochastic knowledge assessment. Methodology, 8, 1222CrossRefGoogle Scholar
Heller, J., Stefanutti, L., Anselmi, P., & Robusto, E. (2015). On the link between cognitive diagnostic models and knowledge space theory. Psychometrika, 80, 9951019.CrossRefGoogle Scholar
Heller, J., Stefanutti, L., Anselmi, P., Robusto, E. (2016). Erratum to: On the link between cognitive diagnostic models and knowledge space theory. Psychometrika, 81, 250251CrossRefGoogle Scholar
Heller, J., Ünlü, A., Albert, D. (2013). Skills, competencies and knowledge structures. In Falmagne, J.-C., Albert, D., Doble, C., Eppstein, D., Hu, X. (Eds.), Knowledge spaces: Applications in education (pp. 229242), Berlin: SpringerCrossRefGoogle Scholar
Hockemeyer, C. (2002). A comparison of non-deterministic procedures for the adaptive assessment of knowledge. Psychologische Beiträge, 44, 495503Google Scholar
Holman, R., Glas, C.A.W. (2005). Modelling non-ignorable missing-data mechanisms with item response theory models. British Journal of Mathematical and Statistical Psychology, 58, 117Google ScholarPubMed
Huebner, A. (2010). An overview of recent developments in cognitive diagnostic computer adaptive assessments. Practical Assessment, Research & Evaluation, 15(3), 17Google Scholar
Junker, B.W., Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258272CrossRefGoogle Scholar
Koppen, M. (1993). Extracting human expertise for constructing knowledge spaces: An algorithm. Journal of Mathematical Psychology, 37, 120CrossRefGoogle Scholar
Koppen, M., Doignon, J.-P. (1990). How to build a knowledge space by querying an expert. Journal of Mathematical Psychology, 34, 311331CrossRefGoogle Scholar
Korossy, K. (1999). Modeling knowledge as competence and performance. In Albert, D., Lukas, J. (Eds.), Knowledge spaces: Theories, empirical research, and applications (pp. 103132), Mahwah, NJ: Lawrence Erlbaum AssociatesGoogle Scholar
Langeheine, R., Pannekoek, J., van de Pol, F. (1996). Bootstrapping goodness-of-fit measures in categorical data analysis. Sociological Methods and Research, 24, 492516CrossRefGoogle Scholar
Lord, F.M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NJ: Lawrence Erlbaum AssociatesGoogle Scholar
McGlohen, M., Chang, H.-H. (2008). Combining computer adaptive testing technology with cognitively diagnostic assessment. Behavior Research Methods, 40, 808821CrossRefGoogle ScholarPubMed
Mislevy, R., & Wu, P.-K. (1996). Missing responses and IRT ability estimation: Omits, choice, time limits, and adaptive testing (Research Report No. RR-96-30-ONR). Retrieved from http://www.ets.org/Media/Research/pdf/RR-96-30.pdf.Google Scholar
Robusto, E., Stefanutti, L., Anselmi, P. (2010). The Gain-Loss Model: A probabilistic skill multimap model for assessing learning processes. Journal of Educational Measurement, 47, 373394CrossRefGoogle Scholar
Rubin, D.B. (1976). Inference and missing data. Biometrika, 63, 581592CrossRefGoogle Scholar
Rupp, A.A., Templin, J. (2008). The effects of Q-matrix misspecification on parameter estimates and classification accuracy in the DINA model. Educational and Psychological Measurement, 68, 7896CrossRefGoogle Scholar
Stefanutti, L., Anselmi, P., Robusto, E. (2011). Assessing learning processes with the Gain-Loss Model. Behavior Research Methods, 43, 6676CrossRefGoogle ScholarPubMed
Stefanutti, L., Robusto, E. (2009). Recovering a probabilistic knowledge structure by constraining its parameter space. Psychometrika, 74, 8396CrossRefGoogle Scholar
Tatsuoka, C. (2002). Data-analytic methods for latent partially ordered classification models. Journal of the Royal Statistical Society Series C (Applied Statistics), 51, 337350CrossRefGoogle Scholar
Tatsuoka, K. (1990). Toward an integration of item-response theory and cognitive error diagnosis. In Frederiksen, N., Glaser, R., Lesgold, A., Safto, M. (Eds.), Monitoring skills and knowledge acquisition (pp. 453488), Hillsdale, MI: Lawrence Erlbaum AssociatesGoogle Scholar
Villano, M. (1991). Computerized Knowledge Assessment: Building the Knowledge Structure and Calibrating the Assessment Routine. Ph.D. Dissertation. New York: New York University.Google Scholar
von Davier, M. (1997). Bootstrapping goodness-of-fit statistics for sparse categorical data: Results of a Monte Carlo study. Methods of Psychological Research, 2, 2948Google Scholar
Xu, X., Chang, H.-H., & Douglas, J. (2003). A simulation study to compare CAT strategies for cognitive diagnosis. Paper presented at the annual meeting of the National Council on Measurement in Education, Chicago.Google Scholar